Question

sin(45+A) cos(45-B)+cos(45+A) sin(45-B)= cos (A-B) prove that

Answer 1

L.H.S

sin(45°+A).cos(45°-B)+cos(45°+A).sin(45°-B),

sin[(45°+A)+(45°-B)],

sin[90°+(A-B)],

cos(A-B),


hence
L.H.S=R.H.S,


since

sinP.cosQ+cosP.sinQ=sin(P+Q),

sin(90°-P)=cosP